Pre-Calc Homework Solutions 269

Pre-Calc Homework - Section 6.5 dP dt 269 18(a 0.0004P(250 0.1 P(250 P 250 k P(M P M P Now find the time to grow from 10,000 bees to 25,000 bees dP

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18. (a) } d d P t } 5 0.0004 P (250 2 P ) 5 } 2 0 5 .1 0 } P (250 2 P ) 5 } M k } P ( M 2 P ) Thus, k 5 0.1 and M 5 250. P 5 } 1 1 M Ae 2 kt } 5 } 1 1 2 A 5 e 0 2 0.1 t } Initial condition: P (0) 5 28, where t 5 0 represents the year 1970. 28 5 } 1 1 25 A 0 e 0 } 28(1 1 A ) 5 250 A 5 } 2 2 5 8 0 } 2 1 5 } 1 1 1 4 1 } < 7.9286 Formula: P ( t ) 5 } 1 1 11 2 1 5 e 0 2 0.1 t /14 } , or approximately P ( t ) 5 } 1 1 7.9 2 2 5 8 0 6 e 2 0.1 t } (b) The population P ( t ) will round to 250 when P ( t ) $ 249.5. 249.5 5 } 1 1 11 2 1 5 e 0 2 0.1 t /14 } 249.5 1 1 1 } 111 1 e 4 2 0.1 t } 2 5 250 } (249.5)( 1 1 4 11 e 2 0.1 t ) }5 0.5 e 2 0.1 t 5 } 55 1 ,3 4 89 } 2 0.1 t 5 ln } 55 1 ,3 4 89 } t 5 10(ln 55,389 2 ln 14) < 82.8 It will take about 83 years. 19. (a) y 5 y 0 e 2 0.01( t /1000) 5 y 0 e 2 0.00001 t (b) 0.9 5 e 2 0.00001 t ln 0.9 52 0.00001 t t 52 100,000 ln 0.9 < 10,536 It will take about 10,536 years. (c) y 5 y 0 e 2 (0.00001)(20,000) < 0.819 y 0 The tooth size will be about 81.9% of our present tooth size. 20.
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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